There was the sound of a glass ceiling shattering last week when Cressida Dick was named as Scotland Yard’s first female Commissioner.

A multitude of other ceilings have been smashed in recent years.

In 2016 Liz Truss was appointed the first female Lord Chancellor. In 2009 Carol Ann Duffy made history when she was named poet laureate.

The Stormont Government has collapsed but until recently the UK, Scottish and Northern Irish administrations were all led by women.

The UK and Scottish Governments are both led by women but Westminster and the Edinburgh Parliament have a long way to go in terms of winning equal representation of men and women (Image: Andrew Milligan /PA Wire)

Such milestones will have triggered the popping of champagne corks. But each celebration is also a reminder that women remain woefully under-represented in so many levels of government, the professions and public life.

It is also sobering to remember that one exceptional individual’s rise to the top of her field in no way means that the systemic factors that hold back so many others have been tackled.

Female representation across the UK

Last year just 7.7% of engineering professionals were women. In other words, 37,000 women were working in this area compared to 438,000 men.

This scale of disparity will horrify people who want their children to grow up in an equal society. But it also bad news for our economy.

Why are there so few women engineers?

The UK desperately needs more engineers. Women are no less adept at problem-solving, planning and design than their male counterparts, so what has stopped so many entering this vital profession?

A mere 17.3% of people working as architects, town planners or surveyors in 2016 were women. When so few of this half of the population are working in a field, it is hard to argue that the country’s most talented individuals are in the top jobs.

The rise in female representation on the boards of FTSE 100 companies has been described as “truly amazing progress”. It’s welcome that by 2015 a quarter of directors in these businesses were women, but can these giant companies claim to have the very brightest minds in critical posts when men overwhelmingly dominate?

This is a problem mirrored across the wider economy. Just 34.8% of all managers, directors and senior officials last year were women.

A 1952 march for equal pay in London

The success of a few brilliant individuals should not be used as evidence that obstacles including subtle discrimination and lingering prejudice are not blocking the progress of millions of others.

Such problems are by no means limited to the private sector.

Women elected to National Assembly

Cressida Dick may be taking the reins of the Met but a paltry 28.6% of police officers in Wales and England in 2016 were women. Only around a quarter of professors were female.

Last year just 10.2% of people in the armed forces are women. The RAF is doing better than other branches, but even there only 14% were female.

The judiciary remains a bastion of maleness. In Wales and England in 2016 just over a quarter of judges were women (27.5%).

Women are in a minority in the judiciary

As the Commons Library analysis points out, in the Council of Europe “only Azerbaijan and Armenia had fewer female professional judges”.

Men are also much more likely to be close to the levers of power in Whitehall. As of March last year, just seven of the 36 permanent secretaries were women.

Women in the Armed Forces

Commons Library

There is an important debate to be had about how to remove barriers and good people often disagree fiercely about the reforms that are needed.

The use of quotas in education and recruitment remains controversial. Better childcare provision could open up new opportunities for women but a recent cross-party report warned that “as long as women continue to take the majority of responsibility for childcare and other forms of unpaid caring, pay differentials will persist”.

A Trafalgar Square demonstration for equal pay in 1969

Nevertheless, this is a challenge that cannot be left for another generation to tackle. A country in which true talent – male or female – is spotted, cultivated and promoted will be a more efficient and equitable one for us all.

We may be moving in the right direction but the pace of progress can seem achingly slow. In the light of the research, can we honestly tell schoolboys and schoolgirls that today they have an equal chance of fulfilling their ambition and potential?

Proportion of female MPs, 1918-2015

The lack of gender balance in politics calls into question the idea that we live in a truly representative democracy.

In the unelected House of Lords this month, only 26% of peers were women. Things were little better in the Commons, where in 2015 a mere 29% of MPs elected were female.

What will it take for near-equal numbers of men and women to win election to this place?

Wales can take pride that it became the only legislature in the UK to have ever achieved gender parity when 30 women were elected in 2003. When Trish Law took Blaenau Gwent in 2006 men were suddenly in the minority.

The Assembly still has the best record for female representation but it has slid back to 42%. That is still ahead of the Scottish Parliament (35%) and the last Northern Ireland Assembly (28%).

The urgent challenge of securing a prosperous future post-Brexit should be the impetus for a radical effort to expand opportunity across the UK so that credible hopes are not crushed and excellence is encouraged at every step.

Just as viewers gawp at how the class system controlled life at Downton Abbey, one day we look back in bewilderment at the cruel forces that sap confidence and hobble aspiration today.